The proof of this theorem was the goal of the author's work [1]}. The proof relies on Riemann–Hilbert problem techniques for inverting singular integral operators
of truncated-Wiener Hopf type along with the Deift-Zhou non-linear steepest descent method [2]}, [3]},
concentration of measure and large deviation techniques
which were developed for dealing with certain
\(\beta \) -ensembles multiple integrals [4]}, [5]}, [6]}, and
some generalisations thereof to the case of \(N\) -dependent integrands in \(N\) -dimensional integrals as it was developed in [7]}.
